Goku's understanding of different universes and races could be deepened in fanfiction. Since Dragon Ball Super introduced the multiverse concept, fanfiction could explore how Goku interacts with and learns from beings from other universes, making him more worldly and less naive in some ways.
One of the interesting power - ups could be his Ultra Instinct form. In fanfiction, it might be further enhanced, like having different levels that are not shown in the original. For example, he could have an Ultra Instinct - Kaioken combination which would be extremely powerful.
One possible fanfiction idea could be that Goku's daughter has unique powers that are a combination of his Saiyan strength and something new, like the ability to control time on a small scale. She might struggle to fit in with the other Z - fighters at first because they see her as just Goku's daughter, but she proves herself by facing a new, powerful enemy that the others can't defeat easily.
In a fanfiction, Goku's daughter might inherit a special power from her mother (who could be an original character in the fanfiction). This power could be related to healing or some kind of spiritual energy. She uses this power to heal the injured during a big battle against a powerful villain. This makes her an important asset to the Z - fighters, not just because of her Saiyan heritage from Goku, but also because of her unique ability.
It's really hard to say. Goku has his Super Saiyan forms which give him incredible power boosts. But Superman has super strength, heat vision, and is nearly invulnerable. In a short fight, Superman might have the edge due to his instant powers like flight and super strength without having to power up. But if Goku manages to reach his higher Super Saiyan forms and uses techniques like the Spirit Bomb, he could potentially defeat Superman.
I think it depends on various factors. Goku's determination and growth are remarkable, but Beerus has an overwhelming level of power and authority that might be difficult to overcome.